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Time of Flight Calculator

When you launch an object into the air—whether it's a ball, arrow, or rocket—gravity pulls it back down. The elapsed time from launch to impact is the time of flight, a key metric in ballistics, sports, and engineering. This calculator determines that duration by combining your initial velocity, launch angle, and starting height into a single computation.

Last updated:

Creators Davide Borchia, PhD
4,159 people find this calculator helpful

Understanding Time of Flight

Time of flight describes the total duration a projectile remains airborne after launch. Unlike simple free fall, projectile motion involves both horizontal and vertical velocity components working simultaneously. The vertical component decreases due to gravity, eventually reversing direction and accelerating downward until the projectile strikes the ground.

The calculation varies depending on launch conditions. An object fired from ground level (height = 0) follows one equation, while launching from an elevated platform requires a different approach. The angle of launch significantly affects flight duration—steeper angles typically extend airtime by directing more velocity upward against gravity.

Real-world applications span ballistic calculations for firearms and artillery, sports physics for basketball and baseball, civil engineering for drainage systems, and aerospace design for rocket trajectories.

Time of Flight Equations

The time of flight depends on the vertical velocity component and initial height. Resolve the launch velocity into horizontal and vertical parts using trigonometry, then apply kinematic equations accounting for gravitational acceleration (9.81 m/s²).

vhorizontal = v × cos(α)

vvertical = v × sin(α)

t = (vvertical + √(vvertical² + 2 × g × h)) / g

  • v — Initial launch velocity in m/s
  • α — Launch angle above the horizontal in degrees
  • h — Starting height above ground level in metres
  • g — Gravitational acceleration, approximately 9.81 m/s²
  • t — Time of flight in seconds

Launch Height and Angle Effects

Starting height dramatically extends flight time. Doubling the launch height does not double the flight duration—the relationship is non-linear because gravity accelerates the falling object. A projectile dropped from twice the height spends approximately 1.4 times longer in the air.

Launch angle influences airtime in a counterintuitive way. A 45° angle maximizes horizontal distance (range), but a steeper angle extends flight time by directing more velocity vertically. An 80° launch produces longer airtime than 45°, though it sacrifices horizontal distance. Conversely, shallow angles below 45° reduce airtime and horizontal range simultaneously.

At 0° (horizontal launch), the full initial velocity contributes to horizontal motion while gravity alone pulls the object downward. This represents the minimum flight time for a given velocity and height.

Common Pitfalls and Caveats

Several factors frequently trip up time-of-flight calculations:

  1. Air resistance is ignored — This calculator assumes a vacuum. Real projectiles slow down due to drag, which reduces horizontal distance and can slightly shorten flight time for steep angles. Sports and long-range ballistics require drag coefficients for accuracy.
  2. Gravitational variation at height — The 9.81 m/s² value is constant near Earth's surface. Rockets and high-altitude applications experience slightly weaker gravity. For most practical cases below 10 km, this difference is negligible.
  3. Ground-level precision matters — Small measurement errors in initial height compound significantly at longer flight times. A 0.5 m error matters less for a 2-second flight but becomes problematic for a 20-second trajectory from a cliff.
  4. Angle measurement reference — Ensure you measure angle from the horizontal ground, not vertically. A 90° angle means straight up; 45° is halfway between horizontal and vertical. Confusion here inverts your results entirely.

Worked Example: Cliff Projectile

Suppose you throw a stone horizontally from a 100 m cliff at 20 m/s. What is its flight time?

Step 1: Identify inputs: v = 20 m/s, α = 0° (horizontal), h = 100 m, g = 9.81 m/s²

Step 2: Calculate velocity components:

  • vhorizontal = 20 × cos(0°) = 20 m/s
  • vvertical = 20 × sin(0°) = 0 m/s

Step 3: Apply the formula:

t = (0 + √(0 + 2 × 9.81 × 100)) / 9.81 = √(1962) / 9.81 ≈ 4.5 seconds

The stone remains airborne for 4.5 seconds, traveling approximately 90 m horizontally before impact. Compare this to dropping the stone straight down (α = 0° without initial velocity)—that would also take 4.5 seconds, confirming that horizontal velocity does not affect flight duration.

Frequently Asked Questions

Why doesn't horizontal velocity affect time of flight?

Gravity acts only vertically, pulling objects downward at a constant rate regardless of sideways motion. Horizontal velocity determines how far the projectile travels, not how long it stays airborne. A stone thrown horizontally and one dropped simultaneously from the same height reach the ground at identical times. The vertical motion equation depends solely on initial vertical velocity, starting height, and gravitational acceleration.

How does increasing the launch angle change flight time?

Steeper launch angles redirect more of your initial velocity upward, fighting gravity longer before the projectile peaks and falls. A 60° launch produces significantly longer airtime than a 30° launch at the same speed. The extreme is 90° (straight up), which maximizes flight time for a given velocity. However, beyond 45°, you sacrifice horizontal distance while gaining height and duration.

What happens when you launch from an elevated platform?

Starting height adds extra time because the projectile must fall that additional distance. The relationship is non-linear—doubling height does not double flight time. Instead, the extra time depends on the square root of the height difference. A 100 m cliff adds roughly 4.5 seconds to flight (assuming horizontal launch), while a 400 m cliff adds roughly 9 seconds, showing the diminishing returns of increased elevation.

Can you use this formula for objects falling straight down?

Yes. A vertical drop is simply a launch with 0° angle and 0 m/s initial velocity. Your formula simplifies to t = √(2h/g). For a 100 m drop, this gives t = √(200/9.81) ≈ 4.5 seconds. This matches free-fall physics precisely and serves as a sanity check for more complex trajectories.

Does the mass of the projectile affect flight time?

No. Neglecting air resistance, all objects fall at the same rate regardless of mass. A bowling ball and a feather launched at identical angles and speeds from the same height will land simultaneously in a vacuum. This counterintuitive result, demonstrated famously on the Moon by Apollo 15, follows directly from gravitational acceleration being independent of mass.

What about very long-range trajectories, like artillery?

Standard time-of-flight formulas assume constant gravitational acceleration and no air resistance. Real artillery accounts for drag (which shortens flight time), varying gravity with altitude, and Coriolis effects. Military ballistics tables use numerical integration and empirical drag coefficients. This calculator works well for laboratory demonstrations, sports, and engineering estimates below a few hundred metres.

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